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Unformatted text preview: a . or E < 0, k i is imaginary, and B/A is xed by the condition that u = AJ i ( ir ) + BJi ( ir ) K i ( r ) is exponentially damped at large r , so the matching condition gives the energy quantization condition. q 2 + 1 / 4 cot q 2 + 1 / 41 / 2 = cot[ ln( a/ 2) ( )] . We have immediately from the scaling periodicity that if is a solution so is n = en/ , where n is any positive or negative integer. In particular there are discrete energy levels extending to . Of course with N nite the above solution breaks down for n N and then one has to go back to the unsimplied matching condition to obtain the quantization condition. * Email address: thorn@phys.uf.edu 1...
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This note was uploaded on 09/25/2011 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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